Question

Prove that the diagonals of a rectangle bisect each other and are of equal length

Answer 1

There is a rectangle ABCD
(I am proving this by congurancy)

In ΔABC & ΔDCB
BC = BC (common)
AB = CD (opposite sides of rectangle are equal)
angle B = C = 90°
By SAS property,
ΔABC = ΔDCB
AC = BD (CPCT) proven

In ΔAOB & ΔCOD
AB = DC (opp sides of rectangle)
angle OAB = OCD (AIA)
angle OBA = ODC (AIA)
By SAS property,
ΔAOB = ΔCOD
OA = OC & OB = OD (CPCT)
Hence, o is mid point of both AC and BD..
AC and BD bisect each other.. proven